Epistemic modals and informational consequence

Schulz, Moritz

doi:10.1007/s11229-009-9461-8

Cited by 15 publications

(14 citation statements)

References 8 publications

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“…That is, the logic of strong assertion is the logic that preserves -validity. Schulz (2010, p. 389) noted the same result about Yalcin’s (2007) informational consequence (IC). That is, iff .…”

Section: Model Theory For Epistemic Multilateral Logicmentioning

confidence: 66%

“…Indeed, epistemic multilateral logic extends the modal logic . Issues for systems dealing with epistemic modality that extend have been recently discussed by Schulz (2010) and Bledin & Lando (2018). We argue that these issues can be dealt with by distinguishing between two notions of proof-theoretic consequence in epistemic multilateral logic (§6).…”

Section: Introductionmentioning

confidence: 99%

“…But another commonly recognized inference allows us to conclude Jane must be at the party from Jane is at the party. It has been argued (see, e.g., Schulz, 2010) that this latter inference, an instance of epistemic strengthening, is importantly different in its logical status from epistemic weakening. Our proof theory will enable us to trace the difference precisely.…”

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confidence: 99%

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Epistemic Multilateral Logic

Incurvati¹,

Schlöder²

2020

The Review of Symbolic Logic

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We present epistemic multilateral logic, a general logical framework for reasoning involving epistemic modality. Standard bilateral systems use propositional formulae marked with signs for assertion and rejection. Epistemic multilateral logic extends standard bilateral systems with a sign for the speech act of weak assertion (Incurvati & Schlöder, 2019) and an operator for epistemic modality. We prove that epistemic multilateral logic is sound and complete with respect to the modal logic $\mathbf {S5}$ modulo an appropriate translation. The logical framework developed provides the basis for a novel, proof-theoretic approach to the study of epistemic modality. To demonstrate the fruitfulness of the approach, we show how the framework allows us to reconcile classical logic with the contradictoriness of so-called Yalcin sentences and to distinguish between various inference patterns on the basis of the epistemic properties they preserve.

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Section: Model Theory For Epistemic Multilateral Logicmentioning

confidence: 66%

Section: Introductionmentioning

confidence: 99%

mentioning

confidence: 99%

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Epistemic Multilateral Logic

Incurvati¹,

Schlöder²

2020

The Review of Symbolic Logic

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“…Thus, from the point of view of modal logic, the above semantics for and ♦ can be summarized as follows: the proposed consequence relation for epistemic modals is the global consequence relation over universal relational models according to the standard semantics (cf. [12]). 2 As for the indicative conditional ⇒, this is where dynamic epistemic logic [5,2] enters the story.…”

Section: Applying Del To Formal Semanticsmentioning

confidence: 99%

Indicative Conditionals and Dynamic Epistemic Logic

Holliday

Icard

2017

Electron. Proc. Theor. Comput. Sci.

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Recent ideas about epistemic modals and indicative conditionals in formal semantics have significant overlap with ideas in modal logic and dynamic epistemic logic. The purpose of this paper is to show how greater interaction between formal semantics and dynamic epistemic logic in this area can be of mutual benefit. In one direction, we show how concepts and tools from modal logic and dynamic epistemic logic can be used to give a simple, complete axiomatization of Yalcin's [16] semantic consequence relation for a language with epistemic modals and indicative conditionals. In the other direction, the formal semantics for indicative conditionals due to Kolodny and MacFarlane [9] gives rise to a new dynamic operator that is very natural from the point of view of dynamic epistemic logic, allowing succinct expression of dependence (as in dependence logic) or supervenience statements. We prove decidability for the logic with epistemic modals and Kolodny and MacFarlane's indicative conditional via a full and faithful computable translation from their logic to the modal logic K45.Logic and the formal semantics of natural language are related by blood and yet somewhat estranged. Today it is rare that formal semanticists consider questions of axiomatizability or decidability of the consequence relations defined by model-theoretic accounts of natural language fragments. Meanwhile logicians focus more on logics motivated by mathematical or philosophical concerns than on logics arising from semantic theories in linguistics.The cost of estrangement is that insights from one field that would be useful for the other may go unnoticed or efforts may be unnecessarily duplicated. The aim of this paper is to help encourage a family reunion between logic and formal semantics of natural language, by way of concrete examples. The topic of modals and conditionals is a prime example of overlap between formal semantics and logic. In this paper, we consider the case of epistemic modals and indicative conditionals.In §1, we show how concepts and tools from modal logic and dynamic epistemic logic can be used to give a simple, complete axiomatization of Yalcin's [16] semantic consequence relation for a language with epistemic modals and indicative conditionals. Then in §2, we show that the formal semantics for indicative conditionals due to Kolodny and MacFarlane [9] gives rise to a new dynamic operator that is very natural from the point of view of dynamic epistemic logic, allowing succinct expression of dependence (as in dependence logic) or supervenience statements. We prove decidability for the logic with epistemic modals and Kolodny and MacFarlane's indicative conditional via a full and faithful computable translation from their logic to the modal logic K45.There are other examples of clear overlap between formal semantics and dynamic epistemic logic, such as the connection between the dynamic logical consequence of [14] and the dynamic consequence of [1], between the notions of epistemic contradictions in [15] and of Moorean sentences i...

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“…This is notwithstanding the fact that axiomatisations for some logics of epistemic modality are available Schulz (2010). showed that the non-implicational fragment ofYalcin's (2007) informational consequence is the logic of S5-validity, i.e.…”

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confidence: 99%

Epistemic Modals in Hypothetical Reasoning

Schlöder

Incurvati

Sbardolini

2022

Erkenn

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Data involving epistemic modals suggest that some classically valid argument forms, such as reductio, are invalid in natural language reasoning as they lead to modal collapses. We adduce further data showing that the classical argument forms governing the existential quantifier are similarly defective, as they lead to a de re–de dicto collapse. We observe a similar problem for disjunction. But if the classical argument forms for negation, disjunction and existential quantification are invalid, what are the correct forms that govern the use of these items? Our diagnosis is that epistemic modals interfere with hypothetical reasoning. We present a modal first-order logic and model theory that characterizes hypothetical reasoning with epistemic modals in a principled manner. One upshot is a sound and complete natural deduction system for reasoning with epistemic modals in first-order logic.

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Epistemic modals and informational consequence

Cited by 15 publications

References 8 publications

Epistemic Multilateral Logic

Epistemic Multilateral Logic

Indicative Conditionals and Dynamic Epistemic Logic

Epistemic Modals in Hypothetical Reasoning

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